Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent variables of DGMs. Existing approaches for performing inference in GP-DGMs do not support sparse GP approximations based on inducing points, which are essential for the computational efficiency of GPs, nor do they handle missing data -- a natural occurrence in many spatio-temporal datasets -- in a principled manner. We address these shortcomings with the development of the sparse Gaussian process variational autoencoder (SGP-VAE), characterised by the use of partial inference networks for parameterising sparse GP approximations. Leveraging the benefits of amortised variational inference, the SGP-VAE enables inference in multi-output sparse GPs on previously unobserved data with no additional training. The SGP-VAE is evaluated in a variety of experiments where it outperforms alternative approaches including multi-output GPs and structured VAEs.

研究了高斯过程深度生成模型中的氐变量的稀疏高斯过程近似的问题，并提出了一种基于部分推理网络的稀疏高斯过程变分自编码器，从而使得稀疏高斯过程能处理多维度的时空数据中缺失的数据，并提高模型的计算效率。